Endogenous Commitment and Nash Equilibria in Competitive Markets with Adverse Selection
19 Pages Posted: 14 Jun 2010
Date Written: June 13, 2010
In this paper, we provide a unified framework for analyzing competitive markets with adverse selection. The key feature of our model is that whether the suppliers of the contracts (uninformed) are committed to the contracts they offer or not is determined endogenously. Because of the endogeneity of the commitment, our model always has a unique Bayesian-Nash equilibrium even though we do not use any refinement to restrict beliefs off-the-equilibrium path. We show that when the Wilson pooling allocation Pareto-dominates the Rothschild-Stiglitz separating allocation the former is the unique equilibrium. We also show that both the non-existence problem in the Rothschild-Stiglitz screening model and the multiplicity of equilibria in the three-stage game of Hellwig are due to the arbitrary restrictions imposed on firms’ actions (strategies).
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